I’ve had good experience with these guys:
As it happens, they seem to have a sale on at the moment too! 50% off any server rental for more than 3 months.
I never really got the chance to use the server as much as I hoped, and never got much use out of it. But I never had any problems with it when I did use it. Easily passworded. Or alternatively, you can set up a list of friends’ accounts, and have the server only let on people whose name is on the list.
I can’t speak for their customer service, as I never had to use it. But I can say their server management software was really good- made installing mods etc really easy. The forum’s full of really useful guides to server stuff. And I remember the server was ready to play on literally a minute or two after I made the order.
I don’t really know much about the disk space, but I find it hard to imagine you would end up with a world save file in the GB range! I can’t think of anything else you’d need hard-drive space for. I think you’d have to do a huge amount of exploration (ie. Make the world really huge) to get a save with that kind of size.
I think it’s RAM which determines how many people the server can handle easily at once. Also, I think some mods increase RAM usage.
If you want want to play with mods, I think you want to look out of servers supporting Bukkit, which is some mod hosting thingymajig.